Optimal Investment under Mutual Strategy Influence among Agents

TL;DR

This paper models the mutual influence among financial agents' investment strategies using a differential game framework, deriving analytical solutions and proposing a fast algorithm, with insights into strategy convergence and impact on wealth.

Contribution

It introduces a novel differential game model for mutual influence in investment strategies, providing analytical solutions and a low-complexity algorithm for approximate solutions.

Findings

Optimal strategies converge to an asymptotic strategy under strong influence.

Strategies are linear combinations of asymptotic and rational strategies.

The proposed algorithm is validated through numerical experiments.

Abstract

In financial markets, agents often mutually influence each other's investment strategies and adjust their strategies to align with others. However, there is limited quantitative study of agents' investment strategies in such scenarios. In this work, we formulate the optimal investment differential game problem to study the mutual influence among agents. We derive the analytical solutions for agents' optimal strategies and propose a fast algorithm to find approximate solutions with low computational complexity. We theoretically analyze the impact of mutual influence on agents' optimal strategies and terminal wealth. When the mutual influence is strong and approaches infinity, we show that agents' optimal strategies converge to the asymptotic strategy. Furthermore, in general cases, we prove that agents' optimal strategies are linear combinations of the asymptotic strategy and their rational strategies without others' influence. We validate the performance of the fast algorithm and verify the correctness of our analysis using numerical experiments. This work is crucial to comprehend mutual influence among agents and design effective mechanisms to guide their strategies in financial markets.